87/89 Additive Inverse :
The additive inverse of 87/89 is -87/89.
This means that when we add 87/89 and -87/89, the result is zero:
87/89 + (-87/89) = 0
Additive Inverse of a Fraction
For fractions, the additive inverse is found by negating the numerator or denominator, but not both. In this case:
- Original fraction: 87/89
- Additive inverse: -87/89
To verify: 87/89 + (-87/89) = 0
Extended Mathematical Exploration of 87/89
Let's explore various mathematical operations and concepts related to 87/89 and its additive inverse -87/89.
Basic Operations and Properties
- Square of 87/89: 0.95556116651938
- Cube of 87/89: 0.93408788187849
- Square root of |87/89|: 0.98870020222899
- Reciprocal of 87/89: 1.0229885057471
- Double of 87/89: 1.9550561797753
- Half of 87/89: 0.48876404494382
- Absolute value of 87/89: 0.97752808988764
Trigonometric Functions
- Sine of 87/89: 0.82911792491884
- Cosine of 87/89: 0.55907375772636
- Tangent of 87/89: 1.4830206452378
Exponential and Logarithmic Functions
- e^87/89: 2.657878079264
- Natural log of 87/89: -0.022728251077556
Floor and Ceiling Functions
- Floor of 87/89: 0
- Ceiling of 87/89: 1
Interesting Properties and Relationships
- The sum of 87/89 and its additive inverse (-87/89) is always 0.
- The product of 87/89 and its additive inverse is: -7569
- The average of 87/89 and its additive inverse is always 0.
- The distance between 87/89 and its additive inverse on a number line is: 174
Applications in Algebra
Consider the equation: x + 87/89 = 0
The solution to this equation is x = -87/89, which is the additive inverse of 87/89.
Graphical Representation
On a coordinate plane:
- The point (87/89, 0) is reflected across the y-axis to (-87/89, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 87/89 and Its Additive Inverse
Consider the alternating series: 87/89 + (-87/89) + 87/89 + (-87/89) + ...
The sum of this series oscillates between 0 and 87/89, never converging unless 87/89 is 0.
In Number Theory
For integer values:
- If 87/89 is even, its additive inverse is also even.
- If 87/89 is odd, its additive inverse is also odd.
- The sum of the digits of 87/89 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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